Stopping Distances

Stopping distance — the total distance covered from the driver seeing a hazard to the vehicle coming to rest. It has two parts.

Thinking distance — the distance travelled during the driver's reaction time, before the brakes are applied. The car does not slow down at all during this time, so

thinking distance = speed × reaction time

Thinking distance is directly proportional to speed.

Braking distance — the distance travelled while the brakes are decelerating the car. From v² = u² + 2as with v = 0, the braking distance is u² / 2a, so braking distance is proportional to the square of the speed.

Example: this is why speed limits matter more than they look. Doubling the speed doubles the thinking distance but quadruples the braking distance. A car at 40 mph does not need twice the stopping distance of one at 20 mph — it needs roughly three times.

What increases thinking distance — tiredness, distraction, alcohol or drugs, and age all lengthen reaction time. Nothing about the car affects it.

What increases braking distance — anything that reduces the braking force or increases the mass: wet or icy roads, worn tyres, worn brakes, a heavily loaded vehicle, and travelling downhill. Note that these are car and road factors, while the thinking-distance factors are all driver factors. Questions frequently test whether you can sort a list into the right column.

Vehicle safety features and stopping — crumple zones, seat belts and airbags do not shorten the stopping distance. They act during the collision, extending the time over which the occupants come to rest and so reducing the force on them, by F = Δp / Δt.

Example: a common exam trap is to ask whether ABS reduces stopping distance. Anti-lock brakes prevent the wheels locking, which keeps the tyres rolling and preserves steering control; on most surfaces they shorten the braking distance, but their main purpose is control, not distance.